Question

Solve the following linear equation:

$x+7-\frac{8x}{3}=\frac{17}{6}-\frac{5x}{2}$

Answer 1

$$\begin{gathered} x+7-\frac{8x}{3}=\frac{17}{6}-\frac{5x}{2} \\ \Rightarrow x-\frac{8x}{3}+\frac{5x}{2}=\frac{17}{6}-7 \end{gathered}$$

On taking LCM on both sides and on solving, we get

$$\begin{gathered} \frac{6x-16x+15x}{6}=\frac{17-42}{6} \\ \Rightarrow 21x-16x=-25 \\ \Rightarrow 5x=-25 \\ \Rightarrow x=\frac{-25}{5} \\ \Rightarrow x=-5 \end{gathered}$$

Hence, $\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathbf{5}$ is the solution of given equation.